The present invention generally relates to the synchronization of sampling rates and system frequency for the analysis of system parameters. More particularly, the present invention relates to synchronizing the sampling rate of an electrical power distribution system to the frequency of the power system.
Protection devices for power systems and equipment typically operate according to protection algorithms based on Fourier analysis of sampled currents and voltages. One possible protection scheme captures instantaneous values, or samples, of power system currents and voltages 64 times per power system cycle, and performs a short term Fourier transform (STFT) on the samples. The calculations are updated in real time every 8 sample periods.
The accuracy of the Fourier algorithm is closely related to the degree of synchronization between the sampling rate and the power system frequency. However, the frequency of the power system is dynamic. For example, under normal load conditions, the frequency of the power system can deviate from a nominal value (e.g., 60 Hz in North America, 50 Hz in Europe and elsewhere) by up to 1 Hz. Under severe overload conditions, when protection is critical, the frequency can drop below nominal by as much as 10 Hz in as little as one second. Upon generator startup, the frequency can ramp up from 0 Hz to the nominal value in less than three seconds. During sudden load rejection, the frequency can overshoot the nominal value by as much as 1.5 times the nominal value. To maintain the accuracy of the Fourier transform calculations, and therefore the reliability of the protection, it is highly desirable to adjust the sampling rate.
Known techniques for adjusting power system sampling rates rely on generating a filtered and squared version of a power system voltage signal, measuring the frequency by counting the zero crossings of the current and voltage signals, and averaging the number of zero crossings over the number of power system cycles. However, such techniques are not sufficiently accurate for a variety of reasons. For example, a current reversal (i.e., where a substantially sinusoidal curve reverses itself just prior to a zero crossing) essentially incurs a xc2xd, period delay and can be incorrectly diagnosed by a zero-crossing algorithm as an underfrequency condition. Further, transients and phase shifts can cause xe2x80x9cfalsexe2x80x9d zero-crossings. In addition, the filtering and squaring circuitry for detecting zero-crossings can introduce noise into the signal in the form of jitter, resulting in additional error. Another shortcoming of techniques that rely on averaging is that the averaging calculation tends to result in a relatively slow synchronization performance.
U.S. Pat. Nos. 5,832,414, 5,832,413, and 5,721,689 disclose a generator protection system and method for phasor estimation and frequency tracking in digital protection systems. The method uses a variable N-point discrete Fourier transform (DFT) to compute phasors based on data acquired from sampled signals. At each sampling interval, the change in phasor angle between the current and previous phasor angles is used to estimate the instantaneous frequency of the signal. Instantaneous frequencies are averaged over a cycle of the signal to generate an average cycle frequency. In addition, a number of discrete frequencies and corresponding DFT windows based on a fixed sampling rate and a predetermined fundamental frequency of the signal are defined and used in estimating the instantaneous frequency. Once the average cycle frequency is determined, the DFT window is adjusted by setting it equal to the DFT window corresponding to the discrete frequency closest to the average cycle frequency. These patents do not adequately address the previously-discussed problems.
U.S. Pat. Nos. 5,671,112 and 5,805,395 disclose systems for implementing accurate V/Hz value measurement and trip time determination for generator/transformer overexcitation protection independent of the conventional frequency tracking and phasor estimation based on DFT techniques. According to the ""112 patent, a sampled sinusoidal voltage signal is passed through a digital integrator and the magnitude of the integrator output is measured as representative of the V/Hz ratio. The digital integrator is implemented in software using a difference equation in a generator protection unit. When the sampling frequency is variable, the filter coefficients of the digital integrator are recalculated each time the sampling frequency is changed, and a new value for the peak magnitude of the output of the digital integrator is calculated using the recalculated filter coefficients.
According to the ""395 patent, a non-recursive digital technique is used which measures the per unit V/Hz value by summing sampled data points every half-cycle of a sinusoidal input signal, and by dividing the sum with an ideal base value sum. When the input voltage signal is sampled at a reasonable frequency, the disclosed technique approximates the per unit V/Hz value of the input voltage signal without computing voltage and frequency separately. The ""112 and ""395 patents likewise do not adequately address the problems described above.
In view of the above discussion, it would be highly desirable to improve the synchronization of the sampling rate of a power system protection device to the power system frequency. It would further be desirable to be able to discriminate between transients and real frequency events, so that transients do not adversely affect the sampling rate while real frequency events will be correctly factored in to adjusting the sampling rate. The present invention overcomes the problems of the prior art and provides additional advantages, by providing for a technique for adjusting the sampling rate of a power system protection device. According to exemplary embodiments, a method for adapting a sampling rate to the frequency of an electrical power system includes the steps of: performing a first frequency calculation; determining first and second derivatives of the frequency of the electrical power system; determining a normal first derivative, a maximum first derivative value and a maximum second derivative value from power system characteristics; comparing the first and second derivatives to the first and second maximum derivative values, respectively, and comparing the first derivative to the normal first derivative; and if the first derivative is less than the normal first derivative, or if both the first and second derivatives are lower than the first and second maximum derivatives, then accepting the first frequency calculation as true, and adapting the sampling rate based on the first frequency calculation.
Techniques implementing the present invention provide greatly improved synchronization, speed, accuracy, and hence protection, over known techniques.